In the circuit shown below,

Question

(a) Write a node equation at node 1 by summing the currents leaving node 1.

(b) Write a node equation at node 2 by summing the currents leaving node 2.

(c) Find V1 and V2 by solving the two node equations.

(d) Find the currents IR1, IR2, IR3, IR4, I5.

(e) Find the power absorbed by R1, R2, R3, R4, and power released by Vs and Is.

Answer 1

R1=2000;R2=3000;R3=500;R4=1000;

Vs=8;Is=4e-3;

3



syms V1 V2

[V1,V2]=solve(-Is+(V1-Vs)/R1+(V1-V2)/R2,...

(V2-V1)/R2+V2/R4+(V2-Vs)/R3,V1,V2);

IR1=(V1-Vs)/R1;

IR2=(V1-V2)/R2;

IR3=(Vs-V2)/R3;

IR4=V2/R4;

I5=IR3-IR1;

PR1=IR1^2*R1;

PR2=IR2^2*R2;

PR3=IR3^2*R3;

PR4=IR4^2*R4;

PVs=-I5*Vs;

PIs=-Is*V1;

Pa=PR1+PR2+PR3+PR4;

Ps=PVs+PIs;

Psum=PR1+PR2+PR3+PR4+PVs+PIs;

V1=vpa(V1,7)

V2=vpa(V2,7)

IR1=vpa(IR1,7)

IR2=vpa(IR2,7)

IR3=vpa(IR3,7)

IR4=vpa(IR4,7)

I5=vpa(I5,7)

PR1=vpa(PR1,7)

PR2=vpa(PR2,7)

PR3=vpa(PR3,7)

PR4=vpa(PR4,7)

PVs=vpa(PVs,7)

PIs=vpa(PIs,7)

Pa=vpa(Pa,7)

Ps=vpa(Ps,7)

Psum=vpa(Psum,7)

Answers:

V1 =

12.0

V2 =

6.0

IR1 =

0.002

IR2 =

0.002

IR3 =

0.004

IR4 =

0.006

I5 =

0.002

PR1 =

0.008

PR2 =

0.012

PR3 =

0.008

PR4 =

0.036

PVs =

-0.016

PIs =

-0.048

Pa =

0.064

Ps =

-0.064

Psum =

0.0